BOSTON — Fauxcahontas put up a new TV ad this week. In it, Liz Warren shares the pain her supposed Indian heritage has caused — why, her parents had to elope because her dad’s family didn’t want their son marrying a girl with Indian blood.

Huh. Twila Barnes, an indefatigable Cherokee genealogist, dug up the 1932 wedding notice in the Oklahoma papers. Warren’s folks got hitched in a large Protestant church 20 miles away, then drove right back to their hometown of Wetumka.

A wedding party was held that evening; Mrs. Warren’s mom’s best friend was a witness. Some elopement.

But Warren, the Democrat aiming to take back Ted Kennedy’s old Senate seat from Scott Brown, has to keep trying to stand up her claim to a few drops of Native American blood — because she’s not going to convince anyone that she didn’t “check the box” to propel herself to success and wealth.

Brown hammered her on it from the start of their first televised debate the other week. Warren’s now a $350,000-a-year tenured professor at Harvard Law, because “she checked the box . . . when she applied to Penn and Harvard, claiming she was a Native American. ”

In other words, this isn’t just the most expensive Senate fight in the nation; it’s now probably the nastiest as well.

Both sides are raising millions — Brown mostly in-state, Warren mostly out-of-state. (Which is weird: Massachusetts has plenty of wealthy liberals.) The polls see-saw — she was ahead in three recent samplings, he was up six in the most recent one.

But the backstory never changes. Warren, an Oklahoma native, was going nowhere in her career until she began “checking the box,” claiming to be an Indian with absolutely no evidence. Once she began listing herself in a minority law-school directory as a woman of color, she catapulted first to the University of Pennsylvania law school, and then to Harvard.

And as soon as she had tenure, Warren abruptly stopped listing herself as a Native-American. Now she claims she’s “Okie to her toes.”

She always points out she never marked the box when applying to college (the University of Houston) or law school (Rutgers). But that proves the point: She never got close to a top-tier school ’til she started exploiting affirmative action.

Her main counterattack is to point out that Brown is a Republican. She’s for Barack Obama and Scott Brown is, have you heard, a Republican.

Given Obama’s likely 60-40 margin in this bluest of states, to survive Brown needs to get at least one of every four or five Barack voters to split their tickets. It’s a tough assignment, but he’s close.

It helps that he has the real hard-scrabble background — in the debate, he mentioned defending his mother when she was attacked by “one of my stepfathers.”

Another problem for Warren: She’s a Harvard prof, as is her tweedy husband, who looks like he was sent over from Central Casting. And, as Brown noted in the debate, “Prof. Warren and her husband make almost three-quarters of a million dollars, Prof. Warren in her instance teaches one class to make over $300,000 in addition to her no-interest ($50,000) loan. . . No wonder [college] costs are so high.”

Warren just got the important endorsement of Boston Mayor Tom Menino, who’s been known to run up 90,000-vote margins in the city for Democrats he likes (which in Warren’s case is still an open question).

But more dirt keeps coming up from Warren’s background. At the debate, Brown sprung a $212,000 fee she got for helping Travelers Insurance in a class-action lawsuit by asbestos workers, who wound up with just $5,555 each. Then he connected her to a $10,000 fee from a bankrupt steel company that Kennedy once denounced on the Senate floor.

And news broke that Warren doesn’t even have a license to practice law in Massachusetts. Now she’s busy explaining why her lucrative legal work wasn’t, well, illegal.